# Problem Set 2

ENGR 1412-00X Software Applications Arkansas State University

Due: 9/7/18

1. Generate data points for the function

y = 4 cos(x) − x2, x = −5.0,−4.5, · · · , 4.5, 5.0

Make a table for the data and format all calculations to 2 decimal places. Chart the results by using an XY scatter plot. Add appropriate title and axis labels. Print the table and chart together on 1 page.

2. The resolution of data can dramatically change the appearance of a graph. If there are too few data points, the plot will not be smooth. If there are too many data points, the time and storage requirements become computationally expensive.

Generate 2 sets of data points for the following functions

f(x) =

{ cos(x) sin(x)

.

Make a table for each of the following data sets, and plot using the 2-D line chart:

(a) Use x = 0, 0.1, 0.2, · · · , 9.9, 10.0 in increments of 0.1. (b) Use x = 0, 1, 2, · · · , 9, 10 in increments of 1.

Label the graphs and print them without printing the tables.

3. Table 1. shows the average daily traffic flow at four different intersections for a six year period.

Create the table above. Plot the data for intersections 1, 3, and 4, but not intersection 2. Use different line types and markers for each of the three lines. Your graph should be a replica of Figure 1. An enlarged version of Figure 1. is included on the final page.

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4. Table 2. is a random collection of student data. Use the data in Table 2. to create a histogram of

students’ GPA.

(a) What percent of students earned a GPA of 3.5 or less?

(b) What percent of students earned a GPA between 2.0 and 3.2?

(c) Create an XY scatter plot of GPA vs Midterms

• Add a trendline to the chart. • Display the equation and R2 values.

(d) Comment on what trendline best fits the data.

(e) Use the trendline equation to predict if the exam score was 96.5.

5. Using the descriptive statistics and GPA data from Table 2, find:

(a) mean, x̄ = 1n ∑n

i=1 xi

(b) sum, ∑n

i=1 xi

(c) count, n

(d) standard deviation, s = √

1 n−1 [

∑n i=1 x

2 i − nx̄2]

(e) the number students GPA’s are within 1 standard deviation of the mean, x̄− s < GPA < x̄+ s.

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6. The Census Bureau has collected data on Arkansas State household owners and found that the average monthly payment is \$1017.31. Given that a mortgage lender has approved a 30 year fixed loan at 5.75% interest, find the principal value financed on the house based on the average monthly payment.

• Include your chart in the printout

7. A cylindrical petroleum tank is to be built to hold 25.0 m3 of hazardous waste. You need to design the tank in a cost efficient manner by minimizing its surface area. Ignore the thickness of the walls in your design.

Recall that the surface area of a right-angled cylinder is

S = 2πr2 + 2πrh

and the volume of a cylinder is

V = πr2h

(a) What are the independent variables?

(b) What are the constraints?

(c) What is the objective?

(d) Based on the objective, write the objective function.

Use Solver to find the tank dimensions that will result in the least surface area. Label your table appropriately.

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